Remark: you are free to propose a preprocessing of the input features, also youre advised to try different values of the learning rate and observe the training curve. Remark: in your code, you are asked to use python, numpy and matplotlib. You shouldnt use libraries like scikit, TensorFlow, pytorch, or any other library dedicated to AI. Remark: Provide an intelligible and commented algorithm that shows your deep understanding of your code.

Exercise 2: The normalized LMS, is a stochastic algorithm derived from the LMS. It consists of normalizing the gradient by the quantity (XT X), so the updating rule becomes: . AW u grad XT X Implement the normalized LMS in the following problem of classification. Step 1: Apply the algorithm normalized LMS to resolve the simplified classification problem. The classification problem has only one perceptron, and classes C1 and C2 correspond respectively to outputs 1 and -1. 1- Provide a figure of the training curve (MSE vs. iteration n). Add a title and names to the axis. 2- After training, write a function "predict to validate the performance of the classifier base on a test dataset, The function should compute and return the False positive, False negative, True positive and True negative. Plot the output of the function predict using PIE, or BAR functions